setwd("C:/Users/marcogeovanni/Desktop/Modern Guide To Econometrics/Chapter 4")
library(readstata13)
Icecream <- read.dta13("icecream.dta") #Utilizamos la base de datos icecream.dta disponible en MIU
summary(Icecream)
## time cons price income
## Min. : 1.00 Min. :0.2560 Min. :0.2600 Min. :76.00
## 1st Qu.: 8.25 1st Qu.:0.3113 1st Qu.:0.2685 1st Qu.:79.25
## Median :15.50 Median :0.3515 Median :0.2770 Median :83.50
## Mean :15.50 Mean :0.3594 Mean :0.2753 Mean :84.60
## 3rd Qu.:22.75 3rd Qu.:0.3912 3rd Qu.:0.2815 3rd Qu.:89.25
## Max. :30.00 Max. :0.5480 Max. :0.2920 Max. :96.00
## temp
## Min. :24.00
## 1st Qu.:32.25
## Median :49.50
## Mean :49.10
## 3rd Qu.:63.75
## Max. :72.00
attach(Icecream)
plot(time, temp/100) # Por motivos de escala se divide la variable temp para poder graficarlo con el resto de variables
lines(temp/100)
lines(cons, col="blue")
lines(price, col="orange") # Al terminar el gráfico se puede ver que los errores parece estar correlacionados con los errores del periodo anterior
E1 <- lm(cons~ price + income + temp) #corremos una regresión para explicar el consumo
summary(E1)
##
## Call:
## lm(formula = cons ~ price + income + temp)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.065302 -0.011873 0.002737 0.015953 0.078986
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1973149 0.2702161 0.730 0.47179
## price -1.0444131 0.8343570 -1.252 0.22180
## income 0.0033078 0.0011714 2.824 0.00899 **
## temp 0.0034584 0.0004455 7.762 3.1e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03683 on 26 degrees of freedom
## Multiple R-squared: 0.719, Adjusted R-squared: 0.6866
## F-statistic: 22.17 on 3 and 26 DF, p-value: 2.451e-07
plot(time, fitted(E1))# graficamos el nuestros valores estimados
lines(fitted(E1))
library(lmtest) # activamos el paquete lmtest para realizar la prueba Durbin-Watson
## Warning: package 'lmtest' was built under R version 3.2.3
## Loading required package: zoo
##
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric
dwtest(E1)# esta es la función de la prueba para autocorrelación
##
## Durbin-Watson test
##
## data: E1
## DW = 1.0212, p-value = 0.0003024
## alternative hypothesis: true autocorrelation is greater than 0
ResidualesE1 <- residuals(E1)#Definimos una variable para guardar los resisudales de E1
LagResidualesE1 <-c(NA, ResidualesE1[1:29])#Definimos esta variable para el lag de los residuales
Aux1 <- lm(ResidualesE1~LagResidualesE1-1)# corremos una regresión auxiliar para hacer pruebas t y X^2
summary(Aux1)
##
## Call:
## lm(formula = ResidualesE1 ~ LagResidualesE1 - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.063581 -0.014006 -0.000714 0.009123 0.080090
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## LagResidualesE1 0.4006 0.1774 2.258 0.0319 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03023 on 28 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.1541, Adjusted R-squared: 0.1238
## F-statistic: 5.099 on 1 and 28 DF, p-value: 0.03192
library("orcutt", lib.loc="~/R/win-library/3.2") #Descargamos el paquete Orcutt
## Warning: package 'orcutt' was built under R version 3.2.3
cochrane.orcutt(E1) #Calculamos GLS de la forma Cochrane.orcutt cuyo estimado es más eficiente bajo condiciones de autocorrelación
## $Cochrane.Orcutt
##
## Call:
## lm(formula = YB ~ XB - 1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.061510 -0.013400 -0.000524 0.013603 0.082052
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## XB(Intercept) 0.1571481 0.2896292 0.543 0.5922
## XBprice -0.8923964 0.8108501 -1.101 0.2816
## XBincome 0.0032027 0.0015461 2.072 0.0488 *
## XBtemp 0.0035584 0.0005547 6.415 1.02e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.03191 on 25 degrees of freedom
## Multiple R-squared: 0.9823, Adjusted R-squared: 0.9795
## F-statistic: 346.9 on 4 and 25 DF, p-value: < 2.2e-16
##
##
## $rho
## [1] 0.4009259
##
## $number.interaction
## [1] 10
temp_1 <- c(NA,temp[1:29])# Con esto construimos el lag de la variable temp, es decir la retrazamos un periodo
E2 <- lm(cons~ price + income + temp + temp_1) #Esta es la nueva especificación incluyendo el Lag de temperatura
summary(E2)
##
## Call:
## lm(formula = cons ~ price + income + temp + temp_1)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.049070 -0.015391 -0.006745 0.014766 0.080892
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.1894822 0.2323169 0.816 0.42274
## price -0.8383021 0.6880205 -1.218 0.23490
## income 0.0028673 0.0010533 2.722 0.01189 *
## temp 0.0053321 0.0006704 7.953 3.5e-08 ***
## temp_1 -0.0022039 0.0007307 -3.016 0.00597 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.02987 on 24 degrees of freedom
## (1 observation deleted due to missingness)
## Multiple R-squared: 0.8285, Adjusted R-squared: 0.7999
## F-statistic: 28.98 on 4 and 24 DF, p-value: 7.099e-09
dwtest(E2)# volvemos a ejecutar otra prueba de Autocorrelación
##
## Durbin-Watson test
##
## data: E2
## DW = 1.5822, p-value = 0.02876
## alternative hypothesis: true autocorrelation is greater than 0